Enter the raw data point, population mean, and standard deviation into the calculator below to determine the z-score, also known as the standard score.
What is a z score?
A z-score, also known as a standard score, is a term used in statistics to describe a signed fractional number of standard deviations by which the value of a data point is above the mean value.
A Z-score is used to compare observational data to theoretical deviation. Determining the z-score require that one knows the mean and standard deviation of a total population that the data in question belongs to.
Since z-score is used to compare observed data to theoretical data, another way of looking at it is to say that it’s a measure of confidence in a data set. This means that z-score directly correlates with a confidence interval
The following formula is used to calculate the z-score:
- Where μ is the mean of the population
- and σ is the standard deviation of the population
- x is the raw data point
The Z score can also be determined using a table such as provided below.
How to calculate a z-score?
The following is a step by step guide on how to calculate the z-score:
- Through analyzing the formula above, we know the first step will be to acquire the mean of the population.
- For this example we will assume the mean is 20.
- The next step is to determine the standard deviation of the population. For this example let’s assume the deviation is 1.5.
- Finally, we must measure our raw data value of x. We find that x is 25.
- The last step is to plug all of this information into the formula above to get our answer. We find the z-score of this problem to be 3.33
Analyze your results and apply to future problems.